Vortex Panel Method: Normal Velocity Geometric Integral [K(ij)]
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- Опубликовано: 20 авг 2024
- We just finished the videos for the source panel method (SPM), and saw its inherent limitations as we looked at some results for an airfoil. Now, to be able to code up the vortex panel method (VPM), we need to compute geometric integrals similar to those for the SPM. These geometric integrals come from the expressions for the normal and tangential velocity.
In this video, we derive the geometric integral from the normal velocity expression (Kij). In the next video, we will derive the geometric integral from the tangential velocity expression (Lij). Finally, we will derive the X and Y velocity expression geometric integrals needed for the streamline calculations, after which we can construct a system of equations to solve for the vortex panel strengths.
===== RELEVANT VIDEOS =====
► Panel Methods Playlist
• How To: Run XFoil from...
===== NOTES =====
- I'll add notes here if I need to.
===== ERRORS =====
- If you see an error in the video, please let me know and I will include it here.
===== REFERENCES =====
Note: the links are Amazon affiliate links. If you do happen to want to buy the book and use the link below, it helps me out a little.
► Fundamentals of Aerodynamics, Anderson
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► Foundations of Aerodynamics, Kuethe and Chow
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► Theory of Wing Sections, Abbott and Doenhoff
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![Vortex Panel Method: Tangential Velocity Geometric Integral [L(ij)]](http://i.ytimg.com/vi/IxWJzwIG_gY/mqdefault.jpg)
![Vortex Panel Method: Tangential Velocity Geometric Integral [L(ij)]](/img/tr.png)
![Source Panel Method: Normal Velocity Geometric Integral [I(ij)]](http://i.ytimg.com/vi/76vPudNET6U/mqdefault.jpg)
![Panel methods [Aerodynamics #11]](/img/1.gif)
wow.. amazing!
greeting from korea. thank you.
Hi Josh, thanks for the upload. I have a question regarding the application of this method to thin airfoil theory.
In the case of modelling a non-cambered airfoil according to thin airfoil theory, the vortex sheet becomes a straight horizontal line. This means phi = 0 and y_i = Y_j for every panel. Therefore, E = 0 for every K_i_j in the computation of the integral in 14:34. Do you have any way of working around this? Or is this method simply not applicable to thin, non-cambered airfoils.
i have the same concern. did you fix this?
@@RainTurtlez Yes I fixed it. I used a model described by Katz and Allen in their book "Low Speed Aerodynamics". I believe the model is mentioned in Chapter 11 of the book. The model is called "the lumped vortex element method".
Hi, Josh. Can you check my e mail I just sent you.